Method of producing a balanced telephone exchange



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A. H. ADAMS METHOD OF PRODUCING BALANCED TELEPHONE EXCHANGE Filed Dec. 27, 1918 2 Sheets-Sheet l Aug 12 v 119% 1,5043%3 A. H. ADAMS METHOD OF PRODUCING A BALANCED TELEPHONE EXCHANGE Filed Dec. 27, 1918 2 Sheets-Sheet. 2

Patented Aug. l2, W21 ie uni "rail.

ARTHUR H. ADAMS,,OE GALION, OHIO, ASSIGNOR TO WESTERN ELE C'I'RIG COMPANY, INCORPORATED, OF NEW YORK, N. Y., CORPORATION 015 NEW YORK.

METHOD OF PRODUCING A BALANCED TELEPHONE EXGHANGE.

Application filed. December 27, 1915. Serial No. 268,525.

To all whom it may concern Be it known that I, Anrrrun H. ADAMS, a citizen of the United States, residing at Galion, in the county of Crawford, State oi Ohio, have invented certain new and use ful Improvements in Methods of Producing a Balanced Telephone Exchange, of which the following is a full, clear, concise, and exact description.

This invention relates to improvements in automatic telephone systems and more, particularly to a trunking arrangement therefor.

The primary object of the present improvement is to provide a universal arrangement of trunks and calling lines so that in any given exchange condition where the average trailic peaks have been estimated, the simultaneous calls will be extended over the smallest number of trunks.

Heretofore telephone systems have been devised employing trunk-s arranged in what is termed a straight group and have also been arranged in what is termed a slipped group.

A straight trunk group is a group of trunks so disposed to the wholeflgroup of lines from which its traffic originates that one trunk is first choice only to all lines;

. another trunk is second choice only to all the lines; a third trunk third choice to all the lines, etc.

A slipped group of trunks a group of trunks so disposed in relation to the whole group of lines whence its trafiic originates that each trunk is first choice to a small number of lines, is second choice to another but equal number of lines, is third choice to another but equal number of lines, etc, and such that all trunks are first, second, third, etc, choices to the same number of lines. I

Carrying the slipped arrangement of trunks a step further, trunks have been arranged in relation to a number of groups of lines, each group containing as before a plurality of smaller groups of lines each containing an equal number of individual lines. In this arrangement a single trunk while being first, second, third choice, etc,

to the small group of lines contained in one large group is also some other numerical choice to the small groups of lines contained in another large group. Due to this latter arrangement the advantages inherent in the usual -slipped trunk arrangement are augmented. I

Heretofore, where the latter slipped trunk arrangement, which will hereafter be termed radically slipped, was employed, exchanges were constructed having either too many or too few trunks to handle the calls in the system, due to the fact that the. arrangement of the number of individual lines in each small group having access to the trunks was merely estimated and the number or trunks necessary for a given number of calling lines was left to speculation. As a consequence, a balanced exchange was never constructed.

In the drawing, Fig. 1 illustrates a typical radically slipped arrangen'ient of calling lines and trunks where the seeking elements attached to the lines are of the return to normal type. Fig. 2 illustrates a typical radically slipped arrangement where the seeking devices remain in their last position where an idle trunk was found. Fig. 3 illus trates a typical straight arrangement of calling lines and trunks. Fig. 4 shows an exchange having two major groups of radically slipped trunks with the trunks of each group or unit radically slipped tothe lines associated with the trunks of the other.

The radical slip is not a specific arrangement of trunks in relation to lines but any arrangement fulfilling a general condition wherein all trunks are symmetrically related to the traliic producing lines.

Furthermore whereas the figures of the drawing for simplicity illustrate only that method of constructing an exchange in which the lines terminate in the active seeking apparatus, the invention is to be understood as equally applicable to that method of constructing an exchange in which the trunks terminate in the active seeking apparatus, as it is clear that with this latter method the trunks can be given the symmet ical and properly proportioned relation of access to the traffic which is the essence of this invention.

The design of a balanced arrangement of trunks and calling lines can only be accomplished by the provision of the correct numerical and access relationship between callinglines and trunks. Hence both the correct number of trunks and also the correct number of lines having access to each trunk must be determined. Since the number of calls entering any exchange and the length of time each call lasts, depend upon the will of the subscribers, "the number of incoming calls and their length of holding time vary widely in difierent localities and in different hours of the day. What number of trunks is necessary for a given number of calling lines must necessarily be determined through the theory of averages and v chance probability.

In designing an exchange, certain factors are always known as, for instance, the number of subscribers lines, the number of access points each line or each trunk may have (in other words the number of points in the seeking element, i. e., line switch, line finder, etc.), and finally the number of lost calls the exchange is willing that the subscribers should sustain. These lost calls. are caused due to a calling line having no idle trunk over which its call may be extended and the number of lost calls permitted in the usual exchange is one in every ten thousand, al-

, though of course this figure is entirely arbitrary.

Other factors though not fixed are through experience and the use of the theory of average estimated substantially accurately, these factors being the number of calls'which enter a given exchange having a given number of calling lines during a busyhour and the average holding time of these calls. With the facts heretofore stated which weredetermined by experience and the application of averages, it is possible to determine the average number of simultaneous calls entering the exchange in a busy period. However, knowing this number in an exchange employing a radical slip, the determination of how many lines to allot to a trunk where the lines for example, have a given number of access points (i. e., the points in the line switch or trunk seeking element) and the number of trunks necessary to extend the calls from the lines in the various parts of the exchange has hereto-' fore been left entirely to speculation, resulting in the production of an exchange which is not balanced and in which there are either too many or an insuflicient number of trunks provided.

In any given exchange condition, a balanced trunking arrangement is produced through the use of the present improvement which is derived and applied as follows:

Where the average calls coming in a time t to one trunk is given, in a pure chance arrangement the average number of calls finding this trunk busy (lost calls) is determined in the following manner.

(1) The average'number of lost calls in period t bears the same ratio to the average total number of calls received in period t as the average time'a trunk is busy in period 25 bears to the total time 25. If we take If to expressed as 9 Reducing this equation to determine the value of L the result is From equation (3) the value of g, which may be taken to represent the average number of calls that find the trunk idle (that is good calls), may be determined. In equa- L tron (2), since the expression 6 represents the number of good calls, where the letter 7 is taken to indicate the number of good calls, from proportion (2) Substituting in this equation the value of L determined in equation (3), equation (4-) becomes 9 (1+1 Considering now the radical slip diagram illustrated in Fig. 1, a trunk X is shown as first choice for each of 1ncom1ng lines 1 to 7 1nclus1ve, as second choice for each of lines '8 to let inclusive, etc. Trunk Y is shown as first choice for lines 8 to 14- inclusive, as second choice for lines 15 to 21 inclusive, etc. Let it be assumed that A represents the average calls per holding time per small group of lines, such as the lines 211 to 217 inclusive or lines 22 to 28 inclusive illustrated in this figure. In this specific diagram seven lines are shown for each small group but this number depends upon the conditions of the exchange and what it should be in a given exchange condition must be determined in order to correctly proportion the number of calling lines in respect to the number of trunks provided for them.

In considering a given exchange condition the assumption is made that for the trallic involved, the number of trunks is suficient, or will be made so, so that it can be stated without sensible error that A, the average calls received at the exchange per holding time per small group of lines, or, as is evi dent from Fig. 1, per trunk, is also the average number of calls handled per holding time per trunk or the average number of good calls which has been previously A is always less than 1. Since the letter .1 and also the letter 9 both represent the number of good calls an equation may be made in which A 9 From equation (5) Substituting for 9 its equivalent value A, the value of a may be stated as which latter expression represents the average calls received overall per trunk per holding time. From equations (8) and the value of L may be stated as A2 FTL which expression represents the average calls lost overall per trunk per holding time.

The proportion of calls that are lost will be the same throughout the length of the trunk. In other words, ii' for example a trunk lost one outo'f every two calls coming to it on the average, it will lose one out of every two of its first hand calls,

one out of every two of its second hand calls, etc. Therefore, 1

y a A (9) FL, where L, represents the average number of first hand calls lost per holding time.

(8) and (9), the value of L, may be stated as:

However, it will be understood that on the average, due to the symmetrical arrange ment of calling lines and trunks, if trunk 1 loses A of its first hand calls per hold in'g time, so will trunk 52, and these will be the second hand calls of trunk 1. The

same ratio L holds true between calls received and calls lost, and an equation may be drawn where the es'pression L represents the average number of second hand calls lost per trunk per holding time. From the equa tions (9), (10) and (11), the 'follcwing equation may be drawn from which the value of L may be found and expressed as is L,=A.3

In similar manner it may be shown that I s 4 i L =A.";

wherefore in an infinite expression If the trunks he slipped n times the last or final average of lost calls per holding time per trunk will be A P. Thls expression, however, is out of A. calls average per trunk per holding time, whence results the average ratio of which expression represents the proportion of calls lost to first hand calls coming to any trunk. As a consequence this expression represents the probability of lost calls. From the foregoing an equation may be written in which A p where 1) indicates the probability of lost calls.

This final equation, Af p is thetundamental equation for calculating the correct or balanced relation between the three quantities:

A or average incoming calls received at the exchange per average holding time of acall per trunk.

n or number o-faccess points of a line to trunks,

79 or percentage of allowable lost calls.

In a 10,000 line exchange having an LU/G11 age of 15,759 calls per busy hour, a holding time of 164 seconds, a probability of lost calls of one in ten thousand, and employing line switches or trunk seeking mechanisms attached to the lines capable of testing in succession twenty-five terminals, 1,000 trunks should be arranged in a radically slipped formation giving access to groups of lines containing 10 individual lines in each group. This arrangement will provide a balanced exchange in whichthe smallest number of trunks are employed to extend the calls coming into the exchange.

This number ol trunks (1,000) and there fore the number of lines per trunk was determined as follows: I

The average number of simultaneous calls in the whole exchange is first derived by dividing 15,759, the number of calls per busy hour, by the number of holding time periods in the hour, which in this case is the quotient of 3600, the seconds in an hour, divided by 164, the seconds of average holding time. The result shows that 717.9 simultaneous calls occur in the entire exchange.

The equation 1. :79 in this case may be expressed as P3 0001, the exponent 25 representing the number of points in the switch or seeking element; and the figure .0001 representing the desired probability a result of 1038, the number of trunks necessary.

Knowing the number of trunks necessary for the exchange, the number of lines required in each group of calling lines is determined by dividing the number of lines in the entire exchange by the number of trunks, or in this case by dividing 10,000 by 1038. This result will not give an integral number of lines per trunk, and the proper procedure in such a case is either to decrease the number of trunks to 1000 giving 10 lines per trunk or to make an approximation which will be exceedingly close, by taking say 1050 trunks and using 10 as the number of lines with first access to 550 trunks and using 9 as the number of lines with first access tothe remaining 500 trunks.

Fig. 2 shows in diagram a radically slipped group of trunks similar to that of Fig. 1, except that it has a smaller number of lines and is equipped with seeking devices which remain in their last position where an idle trunk was found, instead of returning to normal. Fig. 8 indicates the calling lines of an exchange working on the straight slip arrangement, by light vertical lines, and the trunks by heavy horizontal lines. This figure shows that with the straight slip system one trunk serves as first choice forall the lines 1 to inclusive, another as second choice for all of these lines, etc. Fig. 4 illustrates the application of this invention to an exchange in which there are several major groups of trunks, each as large as can be taken care of by a single selecting system. Two such groups B and O are illustrated each consisting of ten trunks X, Y, X Y etc., and in this arrangement each of these trunks serves as first choice for a small group of lines 1 to 7 8 to 15, etc, and as various other choices for other small groups according to any arbitrary symmetrical arrangement. As illustrated, the trunk Y of group B and each of the succeeding trunks of that group is slipped to lines associated with group C and certain of the trunks of group C are slipped back to group B, as for example, the second, third and remaining choice trunks for the lines 1 to 7 inclusive.

From the foregoing it will be seen that the method of producing a balanced exchange in which the smallest number of trunks is employed to extend the calls entering the exchange, is first to so arrange the trunks before the lines or the lines before the trunks that all lines have access to an equal number of trunks, which number for convenience we will term the access number. If seeking mechanisms of the type controlled by the lines are used the access number is equal to the number of points serially arranged in the hunting field of the mechanism. Secondly, the trunks must be symmetrically related to each other as regards access from said lines; and thirdly the number of these trunks must be equal to the quotient of the average number of simultaneous connections required by the lines (in busy periods) divided by a high order root of the allowable maximum percentage of unfulfillable connections, the order of this root being the access number.

Although the present improvement has been illustrated and described as being applied to calling lines and trunks, it is to be understood that the invention is not limited to this specific embodiment but may be applied to any incoming or outgoing telephone lines. The present improvement is also not limited in its application to automatic telephone systems but may also be applied in both semi-automatic and manual systems and in trafiic routing apparatus generally without departing from the scope of the invention,

lVhat is claimed is:

1. The method of economically routing traffic to be distributed over a number oi channels with a given number (01-) oil channels over which any given unit of: the traflic may be rented, a given number (A) oi units of tratfic to be routed per channel per average routing time of a trallic unit, and a given fraction (P) of permissible trallic failures, which method comprises routing the trailic over a total number of channels such as to substantially satisfy the equation 1\.":l.

2. The method of economically routing telephone trafiic at a station over the minimum number of connecting trunks which comprises assigning calls to said trunks in radical slip order and assigning to each trunk a number of calls determined by the equation A:P where A represents the number of calls per trunk per average holding time of a call, it represents the number of access points between each line terminating at the station and the trunks and I represents the permissible fraction of incoming calls lost for want of a connecting trunk.

3. An automatic telephone exchange system having a plurality of trunks, a plurality of incoming lines, and switching mechanism, wherein the number (A) of incoming calls per trunk during the average holding time of a call, the allowable fraction (P) of incoming calls which it is permissible to lose,

and the number (a) of access points of the switching mechanism bear substantially the relation expressed by the equation A P.

4L. A machine switching telephone eX- change unit employing radical slip in which the number (A) of calls originating during the average holding time of a call in the incoming lines for which a single trunk serves as first choice trunk, the allowable fraction (P) of incoming calls which it is number (n) of access points of an individual machine switching mechanism bear substantially the relation expressed by the equation A P.

6. A machine switching telephone system employing radical slip having such a number of trunks that the number (A) of calls originating on the average during the average holding time of a call in the incoming lines for which a single trunk serves as first choice trunk, the allowable fraction (P) of incoming calls which it is permissible to lose, and the number (n) of access points of an individual switching mechanism bear substantially the relation A zP.

In witness whereof, I hereunto subscribe my name this 26th day of November A. D., 1918.

ARTHUR H. ADAMS 

